On solvability of dissipative partial differential-algebraic equations
Functional Analysis
2022-04-25 v1 Analysis of PDEs
Optimization and Control
Abstract
In this article we investigate the solvability of infinite-dimensional differential algebraic equations. Such equations often arise as partial differential-algebraic equations (PDAEs). A decomposition of the state-space that leads to an extension of the Hille-Yosida Theorem on Hilbert spaces for these equations is described. For dissipative partial differential equations the famous Lumer-Phillips generation theorem characterizes solvability and also boundedness of the associated semigroup. An extension of the Lumer-Phillips generation theorem to dissipative differential-algebraic equations is given. The results is illustrated by coupled systems and the Dzektser equation.
Cite
@article{arxiv.2204.10599,
title = {On solvability of dissipative partial differential-algebraic equations},
author = {Birgit Jacob and Kirsten Morris},
journal= {arXiv preprint arXiv:2204.10599},
year = {2022}
}